RELATIVE COMPLEXITY OF RANDOM WALKS IN RANDOM SCENERY IN THE ABSENCE OF A WEAK INVARIANCE PRINCIPLE FOR THE LOCAL TIMES

• 成果类型: Article
• 署名作者: Deligiannidis, George; Kosloff, Zemer
• 署名单位: University of Oxford; University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1118
• 发表日期: 2017
• 页码: 2505-2532
• 关键词: measure-preserving transformations; 2-dimensional random-walks; loosely bernoulli; limit-theorem; entropy; Generators

摘要

We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Folner property almost surely.